Automatic handwriting recognition using both static and dynamic parameters

ABSTRACT

Methods and apparatus are disclosed for recognizing handwritten characters in response to an input signal from a handwriting transducer. A feature extraction and reduction procedure is disclosed that relies on static or shape information, wherein the temporal order in which points are captured by an electronic tablet may be disregarded. A method of the invention generates and processes the tablet data with three independent sets of feature vectors which encode the shape information of the input character information. These feature vectors include horizontal (x-axis) and vertical (y-axis) slices of a bit-mapped image of the input character data, and an additional feature vector to encode an absolute y-axis displacement from a baseline of the bit-mapped image. It is shown that the recognition errors that result from the spatial or static processing are quite different from those resulting from temporal or dynamic processing. Furthermore, it is shown that these differences complement one another. As a result, a combination of these two sources of feature vector information provides a substantial reduction in an overall recognition error rate. Methods to combine probability scores from dynamic and the static character models are also disclosed.

This is a divisional of application Ser. No. 08/009,515 filed on Jan.27, 1993, now U.S. Pat. No. 5,491,758.

FIELD OF THE INVENTION

This invention relates to apparatus and methods for automaticallyrecognizing handwriting.

BACKGROUND OF THE INVENTION

Symbols formed by handwriting, when traced on an electronic tablet, arerepresented by sequences of x-y coordinate pairs. A fundamental unit ofhandwriting is the stroke. A stroke is considered as a sequence ofpoints, represented by their respective x-y coordinates. Symbols, suchas letters of the alphabet and numbers, are assemblages of such strokes.

Desirable features of an automatic handwriting recognition systeminclude an ability to process the input data so as to minimizeredundancies, and to also model the data by means of robust statisticaltechniques. Parameters that are considered are typically dependent onthe direction of pen movement. That is, the temporal order of the pointsis preserved when deriving feature vectors. The rational for preservingthe temporal ordering of the stroke data is that there is a degree ofconsistency in the way characters are formed by a given writer. Forexample, the letter "O" may be written either in a clockwise orcounter-clockwise motion. By allowing for these two possibilities, andretaining the direction of pen movement, it is possible to design arecognition system that is robust with respect to noise because theoverall temporal trace of the system is not affected by smallfluctuations. Furthermore, it is often possible to distinguish betweensimilar shapes, such as an `S` formed with one stroke and a `5` that isformed with two strokes, by virtue of the number of strokes and/or thedirection of pen movement.

However, a handwriting recognition system that is dependent solely uponstroke order may exhibit certain deficiencies. One such deficiency is adifficulty in properly handling delayed strokes, such as the crossing ofa `t` and the dotting of an `i` or a `j`. Retraces of characters mayalso present difficulties. Another deficiency of handwriting recognitionsystems that process only temporal, or dynamic, input data is anambiguity that is introduced when modeling multi-stroke characters, suchas capital letters. This ambiguity exists because the number ofrepresentations of such multi-stroke characters increases geometricallywith the number of strokes. Finally, there may be little consistencyamong different writers in the direction of pen movement. It istherefore necessary to incorporate a large number of characterprototypes or templates, to achieve reasonable writer independentrecognition performance. However, the use of a large number of templatesincreases both the memory requirements of the handwriting recognitionsystem and also the processing time that is required to search throughthe templates to find a most probable match with an input character.

It is an object of this invention to provide a handwriting recognitionsystem that employs both dynamic (temporal) feature vectors and static(spatial) feature vectors when recognizing handwriting.

A further object of this invention is to provide a handwritingrecognition method and apparatus that operates in a parallel manner tosimultaneously provide both dynamic and static feature vectors inresponse to input signals from a handwriting transducer.

Another object of this invention is to provide a method and apparatusfor deriving static feature vectors that are usable both with on-line,real time handwriting recognition techniques and also with off-line,non-real time techniques, such as in optical character recognitionsystems.

SUMMARY OF THE INVENTION

The foregoing and other problems are overcome and the objects of theinvention are realized by methods and apparatus for the automaticrecognition of handwritten text that employs the use of both dynamic andstatic parameters. It is shown that the errors produced by these twomethods are to a great extent orthogonal and, consequently, acombination of the two sets of parameters greatly reduces the overallhandwriting recognition error rate.

The teaching of this invention resolves some of the problems associatedwith dynamic feature selection, while at the same time retaining themajor advantages of dynamic feature selection. A feature extraction andreduction procedure is disclosed that relies principally on the staticor shape information, wherein the temporal order in which the points arecaptured by the tablet may be disregarded. Thus, only the shape of thecharacter is considered. This is achieved by generating and processingthe data with three independent sets of feature vectors which encode theshape information of the input character information. These featurevectors include horizontal (x-axis) and vertical (y-axis) slices of abit-mapped image of the input character data, and an additional featurevector to encode an absolute y-axis displacement from a baseline of thebit-mapped image.

It is shown that the recognition errors that result from the spatial orstatic processing are quite different from those resulting from temporalor dynamic processing. Furthermore, it is shown that these differencescomplement one another. As a result, a combination of these two sourcesof feature vector information provides a substantial reduction in anoverall recognition error rate. It is also shown that the method of thisinvention works well both for writer dependent and writer independentrecognition modes. In the latter case, the resulting accuracy issignificantly improved over that obtained with refined dynamic modelingtechniques.

The method of this invention is logically divided into two operations. Afirst operation is a training phase wherein estimates of the parametersof a character model are obtained. A second operation is a decodingphase which recognizes incoming unknown handwriting-generated signals.Methods to combine probability scores from the dynamic and the staticcharacter models are also disclosed.

BRIEF DESCRIPTION OF THE DRAWINGS

The above set forth and other features of the invention are made moreapparent in the ensuing Detailed Description of the Invention, when readin conjunction with the attached Drawings, wherein:

FIG. 1 provides examples of five different types of handwriting;

FIG. 2 is a block diagram of a generalized handwriting recognitionsystem emphasizing training and decoding paradigms;

FIG. 3 is a block diagram of a handwriting recognition system accordingto the present invention;

FIG. 4 is a detailed block diagram of the front-end parameter extractionblock which is shown generally in FIG. 3;

FIG. 5 illustrates a ballistically spaced character which in input tothe pre-filtering block of FIG. 4;

FIG. 6 illustrates an equally spaced character which is output from thepre-filtering block of FIG. 4;

FIG. 7 illustrates how the top 1/4 of the ballistically spaced characterof FIG. 5 is transformed to the equally spaced character of FIG. 6;

FIG. 8 is a flow chart detailing how the pre-filtering block of FIG. 4functions to transform the ballistically spaced character of FIG. 5 tothe equally spaced character of FIG. 6;

FIG. 9 illustrates a sampled character for which a spatial featurevector is obtained;

FIG. 10 is a flow chart illustrating a spatial feature vector extractionmethod;

FIG. 11 illustrates a portion of a handwritten character being processedto generate a first parameter vector for a point (P);

FIG. 12 illustrates a six dimensional local parameter vector generatedfor the point (P) of FIG. 11 by collecting a plurality of local spatialattributes;

FIG. 13 illustrates a handwritten character being processed to generatea second parameter vector for a point (P);

FIG. 14 illustrates a three dimensional global parameter vectorgenerated for the point (P) of FIG. 13 by collecting a plurality ofglobal spatial attributes;

FIG. 15 illustrates how windowing is accomplished on a character byconcatenation of individual parameter vectors as extracted in FIGS. 12and 14;

FIG. 16 is a flow chart detailing how the windowing block of FIG. 4functions to perform the concatenation of the parameter vectorsillustrated in FIG. 15 and thereby produce spliced vectors;

FIG. 17 is a flow chart detailing how the projection block of FIG. 4functions to produce a feature vector from the spliced vectors obtainedin FIG. 16;

FIG. 18 is a detailed block diagram of the dynamic prototypeconstruction block of FIG. 3;

FIG. 19 is a diagram illustrating K-means clustering;

FIG. 20 is a flow chart detailing how the Euclidean K-means clusteringblock of FIG. 18 functions;

FIG. 21 is a flow chart detailing how the Gaussian K-means clusteringblock of FIG. 18 functions;

FIG. 22 is a flow chart detailing how the dynamic likelihood estimatorblock of FIG. 3 functions; and

FIG. 23 is a flow chart detailing how the decoder block of FIG. 3functions for the case of dynamic feature vectors.

DETAILED DESCRIPTION OF THE INVENTION

A presently preferred embodiment of this invention employs techniques toprocess handwriting input, specifically dynamic (temporal) processing ofthe handwriting input, that are disclosed in commonly assigned U.S.patent application Ser. No. 07/785,642, filed Oct. 31, 1991, now U.S.Pat. No. 5,343,537, entitled "A Statistical Mixture Approach toAutomatic Handwriting Recognition", by J. Bellagarda, E. Bellagarda, D.Nahamoo and K. Nathan. The present invention extends this teaching bythe use of static, shape-based character feature vectors, and by acombination of static and dynamic feature vectors.

In handwriting recognition, handwritten characters generally fall intofive groups depicted in FIG. 1, the groups being depicted in increasingorder of recognition complexity. Specifically, these groups include afirst type of writing (W1) known as box discrete wherein individualcharacters are formed within predefined areas, or boxes, therebysimplifying the task of character segmentation. A second type of writing(W2) is known as spaced discrete wherein the user intentionally formseach character such that no character touches another. A third type ofwriting (W3) is known as run-on discrete wherein the user may formcharacters that touch or "run-on" to, one another. A fourth type ofwriting (W4) is cursive writing where the user normally writes the wholeword as a series of connected letters, and then subsequently crosses thet's and dots the i's and j's. Finally, a fifth type of writing (W5) isunconstrained writing wherein the user may use a mixture of run-on andcursive writing. The last type is most difficult and presents the mostcomplex segmentation and recognition task of the five styles depicted inFIG. 1.

Referring to FIG. 2 there is illustrated, in block diagram form, ahandwriting recognition system that is constructed in accordance withthis invention. A generalized discussion of FIG. 2 is first provided,followed by a detailed description of the operation of each of theblocks shown therein. At block 2 there occurs data acquisition of stylusor pen stroke information. Acquired strokes are operated on to recognizethe handwriting information. During a training mode of operation, asshown at block 4, the acquired handwriting information is analyzed, inreference to a known, training script, to train the underlying modelspurporting to represent this information. During use, the modelparameters obtained during training are used by decoding block 6,together with feature vectors corresponding to the (unknown) handwritingto be recognized.

Recognized handwriting is thereafter made available for use by block 8.By example, a recognized message may be simply converted to analphanumeric format and displayed upon a display device. The recognizedmessage may also be provided to any application that wouldconventionally receive messages from a keyboard such as, by example, aword processing system.

FIG. 3 is a block diagram of a handwriting recognition system thatimplements the methods of the invention that are described below. A dataprocessing system 10, which for any example may be an IBM 3090/VF or anIBM RS 6000, receives character or stroke information produced by a userusing a handwriting transducer, typically a stylus 12 that writes on anelectronic tablet 14. The character or stroke information may bedisplayed on the electronic tablet 14 or another display device (notshown). The computer 10 can be used either in a training mode 16 or in adecoding mode 18.

In either the training mode 16 or the decoding mode 18 a front-endparameter extraction block 22 is employed. In accordance with thisinvention, the front-end parameter extraction block is operable forextracting both dynamic (temporally-based) feature vectors and alsostatic (shape-based or spatially-based) feature vectors from the outputof the tablet 14.

In the training mode 16 the system includes a dynamic prototypeconstruction block 24a and also a static prototype construction block24b. In the decoding mode 18 the system includes a dynamic likelihoodestimator 28a, a static likelihood estimator 28b, an overall (combined)likelihood estimator 28c, and a decoder 30 that operates with a languagemodel block 26.

The blocks 22-30 are shown as functional program modules, however, it isto be appreciated that some or all of these functional blocks may beimplemented in hardware form instead of software form.

The front-end parameter extraction block 22 provides dynamic and staticfeature vectors to the prototype construction blocks 24a and 24b,respectively, during the training mode 16, or to the likelihoodestimator blocks 28a and 28b, respectively, during the decoding mode 18.

Dynamic Feature Vector Extraction

With respect to dynamic feature vector extraction, the parameterextraction block 22 operates in accordance with the following ninemethod steps.

1. Perform a pre-filtering of the data to normalize for the speed ofwriting. This is accomplished by converting the time-dependentrepresentation captured by the tablet 14, where the spacing betweenpoints is ballistic in nature, into a time-independent representation,where all the points are equally spaced. Linear-interpolation isperformed as necessary to find the resulting equally spaced points. Ifdesired, a cubic spline interpolation can also be performed for a morerefined interpolation.

2. For each point P_(n) of coordinate (x_(n),y_(n)) in the trainingdata, form a P-dimensional vector p_(n) of feature elementsrepresentative of the local pen trajectory around P_(n). For example, agood choice for P is 6, with feature elements given by:

(i) the horizontal and vertical incremental changes:

    Δx.sub.n =x.sub.n -x.sub.n-1, Δy.sub.n =y.sub.n -y.sub.n-1 ;

(ii) the sine and cosine of the angle of the tangent to the pentrajectory at P_(n) : ##EQU1## and (iii) the incremental changes in theabove two parameters:

    Δcosθ.sub.n =cosθ.sub.n+1 -cosθ.sub.n-1, Δsinθ.sub.n =sinθ.sub.n+1 -sinθ.sub.n-1.

It should be noted that the last two parameters provide informationabout the curvature of the pen trajectory at point P_(n).

3. For each point P_(n) of coordinates (x_(n),y_(n)) in the trainingdata, form a P'-dimensional vector P'_(n) of feature elementsrepresentative of the global pen trajectory up to P_(n). For example, agood choice for P' is 3, with feature elements given by: (i) the heightfrom the baseline y_(n), (ii) the width from the beginning of the strokex_(n) -x_(i), where x_(i) is the first coordinate of the current stroke,and (iii) the inter-stroke distance if the current character is composedof more than one stroke.

4. For each stroke in the training data, determine a subset of thepoints P_(n) in that stroke, say Q_(i), with the property that the Q_(i)'s are approximately equally spaced. This set includes the first andlast points of each stroke, and the spacing interval is some reasonablefunction of the line height.

5. At each location Q_(i) obtained in Step 4, construct a Q-dimensionalspliced vector by concatenating together the H vectors p_(n) precedingQ_(i), the vector q_(i) corresponding to Q_(i), and the H vectors p_(n)following Q_(i). Similarly, construct a Q'-dimensional spliced vector byconcatenating together the H' vectors p_(n) preceding Q_(i), the vectorq_(i). corresponding to Q_(i) and the H' vectors p'_(n) following Q_(i).This is realizable provided the following is true:

    Q=P(2H+1), Q'=P'(2H'+1).

Suitable choices are H=H'=20, yielding values Q=246 and Q'=123.

6. Compute the mean vector and covariance matrix of all theQ-dimensional vectors corresponding to local handwriting features.Denote these as M_(t).sup.(1) and S_(t).sup.(1), respectively.Similarly, compute the means vector and covariance matrix of all theQ'dimensional vector corresponding to global handwriting features.Denote these are M_(t).sup.(2) and S_(t).sup.(2), respectively.

7. For n=1,2 compute E_(t).sup.(n), the eigenvector matrix ofS_(t).sup.(n) and A_(t).sup.(n) the diagonal matrix of correspondingeigenvalues. It is noted that these quantities obey the relationship:

    S.sub.t.sup.(n) =E.sub.t.sup.(n) Λ.sub.t.sup.(n) E.sub.t.sup.(n) T,

where T denotes matrix transposition. Thus, the leading eigenvectors inE_(t).sup.(n) correspond to the leading eigenvalues in Λ_(t).sup.(n).

8. Using the R₁ leading eigenvectors from Step 7, project theQ-dimensional feature vectors of Step 5 onto a space of dimension R₁.Designate the resulting vectors r_(i).sup.(1). A reasonable value for R₁is 6. At this point the redundancy present in the Q-dimensional splicedfeature vectors has been eliminated by concentrating on the mostinformative feature elements. The space spanned by the vectorsr_(i).sup.(1) is referred to as the chirographic space C.sup.(1).

9. Similarly, using the R₂ leading eigenvectors from Step 7, project theQ'-dimensional feature vectors of Step 5 onto a space of dimension R₂,with resulting vectors r_(i).sup.(2). A reasonable value for R₂ is 15.Note that R₂ >R₁ because there is generally less redundancy present inthe (global features) Q-dimensional spliced feature vectors than in the(local features) Q-dimensional spliced feature vectors. The spacespanned by the vectors r_(i) ² is referred to as the chirographic spaceC.sup.(2).

The prototype construction block 24a performs the following Steps 10-14of the handwriting recognition method to produce (i) chirographicprototypes representing suitable portions of characters and (ii) mixturecoefficients indicating how to combine the chirographic prototypes. Thisinformation is used in the decoding mode to determine, or recognize,unknown characters. The language model block 26 provides language modelprobabilities which may be used to determine what characters are mostlikely to occur in a given context.

Dynamic prototype construction method Steps 10-15 are set forth below.

10. Repeat this step for n=1,2. Starting with random clusterassignments, perform K-means Euclidean clustering of the projectedvectors r_(i).sup.(n) obtained in Steps 8 and 9, so as to obtainpreliminary prototype distributions in the corresponding R_(n)-dimensional chirographic space.

11. Repeat this step for n=1,2. Starting with the preliminarydistributions of Step 10, perform K-means Gaussian clustering of theprojected vectors r_(i).sup.(n) obtained in Steps 8 and 9, so as toobtain final Gaussian prototype distributions in both chirographicspaces. Denote these prototype distributions as π_(k).sup.(n) and usecluster sizes to estimate the prior probability Pr(π_(k).sup.(n)) ofeach prototype distribution in the respective R_(n) -dimensionalchirographic space.

12. Repeat this step for n=1,2. Using the Gaussian distributions fromStep 11, compute, for all vectors r_(i).sup.(n) obtained in Steps 8 and9, the quantity Pr(r_(i).sup.(n) |π_(k).sup.(n)). Also estimate theprobability of each feature vector as: ##EQU2## assuming the totalnumber of clusters in the respective chirographic space is K_(n). Goodchoices are K₁ =K₂ =400.

13. Repeat this step for n=1,2. Using the results of Steps 11 and 12,compute the quantity: ##EQU3## and note against which character a_(j),in the vocabulary considered, that each vector r_(i).sup.(n) is alignedwith in the training data.

14. Repeat this step for n=1,2. For each character a_(j) in thevocabulary considered, pool together all the r_(i).sup.(n) which havebeen aligned against it and accumulate the correspondingPr(π_(k).sup.(n) | r_(i).sup.(n)). After normalization, this provides anestimate of Pr(π_(k).sup.(n) |a_(j)), the prior probability of eachprototype distribution in the respective chirographic space given eachcharacter a.sub. j. This completes the training phase.

15. Repeat steps 1-5 and 8-9 on test data, so as to produce test featurevectors in the same respective chirographic spaces as the training data.

In the absence of the static feature vector determination that isdescribed in detail below, the following Step 16 is employed torecognize a most likely character that the dynamic feature vectorsrepresent. More specifically, during the recognition mode the dynamiclikelihood estimator 28a, which performs Step 16 of the handwritingrecognition method, receives dynamic feature vectors from block 22 whichhave been produced from the unknown strokes or characters to berecognized. These dynamic feature vectors lie in the same chirographicspace(s) as the chirographic prototypes from block 24a, and cantherefore be compared to each of them to evaluate the contribution ofeach of them to each particular feature vector. This information isintegrated using the mixture coefficients produced during training tocompute the likelihood that each particular feature vector "belongs" toa character in the alphabet. Over all the feature vectors, this can beused to produce candidate characters for recognition to decoder 30.Decoder 30 integrates into the overall score the language modelprobabilities from block 26 corresponding to the maximum score.Recognized handwriting is then produced at output 32 of decoder 30. Therecognized handwriting may be displayed on the tablet 14, or may beprovided to a utilization device 33, which for example may be a displaydevice, printer, application program or the like.

16. For each frame of data f_(i) represented in the chirographic spaceC.sup.(1) by r_(i).sup.(1) and in the chirographic space C.sup.(2) byr_(i).sup.(2), use the Gaussian mixture distributions obtained in Step11 and the prior probabilities obtained in Step 14 to form the quantity:##EQU4## i.e., the weighted product of two single Gaussian mixturedistributions covering the entire chirographic label alphabet. In thisexpression, alpha controls the influence of the second codebook relativeto the first. A suitable value for alpha is 0.7. It remains to multiplythe scores of successive frames to obtain the overall score for atentative sequence of frames, thus completing the decoding process forthe case where only dynamic feature vectors are employed.

However, an important aspect of this invention is the use of staticfeature vectors to complement the dynamic feature vectors that aredescribed above. As such, the operation of the system 10 for derivingand using both static and dynamic feature vectors is described belowwith respect to a presently preferred method of the invention.

Static Feature Vector Extraction

Reference is made to the flow chart of FIG. 10 for the description ofSteps 1-11, wherein the blocks are designated as 10-1 for Step 1, 10-2for Step 2, etc.

1. Increase the resolution of the x and y traces obtained by the tablet14 by interpolating by means of cubic splines. This step corresponds to,and may be performed in an identical fashion to, the Step 1 of thedynamic feature vector extraction method described above.

The following Steps 2-11 describe the operation of the front-endparameter extraction block 22 when extracting static feature vectors,specifically blocks 36b, 36c, and 36d of FIG. 4. Reference is also madeto sample handwritten character "a" that is shown in FIG. 9.

2. Sort the resulting x,y pairs in terms of ascending x values. Thisenforces a left to right structure on the input text. Alternately, aright to left structure can be imposed on the input text by sorting interms of descending x values.

3. Sample the image along the x direction at intervals of δx. Thisyields a sequence of the form {x_(i) }, where x_(i) =x_(i-1) +δx.

4. For each sample point x_(i) define a slice of width 1w centered onthat sample. Associate all y values within this width with that sample.A reasonable value for 1w is 1.5 δx. This yields a vector of the formy(x_(i)).

5. Quantize the range of y values to n_(y) equispaced levels, l_(k). Foreach x_(i) assign all y's associated with it to one of these levels;i.e.

    yεl.sub.k ⃡l.sub.k-1 Δl<y<l.sub.k Δl,

where Δl=(ymax-ymin)/n_(y). A reasonable value for n_(y) is 8.

6. For each x_(i) construct a feature vector fx(x_(i)) of length n_(y),such that the kth element is one if at least one y was assigned tol_(k), and zero otherwise. This can be viewed as constructing a bitmapof the slice with grid size n_(y). It should be noted that it is alsopossible to encode some dynamic information within the static frameworkby defining three possible states for each element of f_(x) (x_(i)).That is, (0,0) in the absence of a point, (-d,1) for a point with a leftto right stroke direction and (d,1) for a point with a right to leftstroke direction. This is meaningful provided that d is less than thesquare root of 1/3. The choice of d affects the degree to which thetemporal information is utilized. This tri-state parameterization of thebitmap results in an increase in performance. This representationsimultaneously embodies both spatial and temporal information. It isalso possible to encode additional information regarding the strokedirection in this fashion, e.g., to quantify the angle of the stroke(Freeman coding).

7. For each x_(i), construct another feature vector of length 1, f_(cg)(x_(i)) such that: ##EQU5## where the summation is over all y's withinthe slice associated with x_(i).

8. Determine a subset of points of {x_(i) } such that the points arespaced Δx apart. Define these points as {X_(i) }. By example, Δx istaken to be 1.5 δx.

9. At each location X_(i) construct a N dimensional spliced vector byconcatenating together H_(x) feature vectors f_(x) preceding the currentpoint X_(i), the feature vector f(X_(i)) at the current point, and theH_(x) feature vectors succeeding X_(i). This yields a spliced featurevector, F(x_(i)), of length:

    N=n.sub.y (2H.sub.x +1).

A good choice for H_(x) is 9.

10. Repeat Step 9 for f_(cg) (x_(i)) to obtain F_(cg) (x_(i)). At thecompletion of Step 9, the input bitmap has been scanned in the x-axisdimension. Step 11 is next executed so as scan the bitmap in the y-axisdimension.

11. Repeat steps 2 through 6 and 8 through 9 for the y dimension, i.e.form horizontal slices at equispaced intervals along the y dimension.The corresponding values of δy and Δy are equal to those of δx and Δx,respectively. The width of the slice is also the same. It has been foundthat quantizing the horizontal slice to fewer levels than the verticalslice is preferable. An exemplary value for n is 6, with H_(y) chosen tobe 11. This yields an analogous feature vector, F_(y) (Y_(i)).

Steps 12 through 19 are performed for each of the three classes offeature vectors, or codebooks, in a similar manner to that describedabove with respect to Step 6 through Step 14 of the dynamic featurevector extraction method.

12. Compute the mean vector and covariance matrix of all the splicedvectors of a given codebook. Denote these as M_(d) and S_(d),respectively.

13. Compute E_(d), the eigenvector matrix of S_(d), and Λ_(d), thediagonal matrix of corresponding eigenvalues. It is noted that thesequantities obey the relationship:

    S.sub.d =E.sub.d Λ.sub.d E.sub.d.sup.T,

where ^(T) denotes transposition. As a result, the leading eigenvectorsin E_(d) correspond to the leading eigenvalues in Λ_(d).

14. Using the R leading eigenvectors from Step 13, project theN-dimensional feature vectors of Step 9 onto a space of dimension R.Call the resulting vectors r_(i). At this point the redundancy presentin the N-dimensional spliced feature vectors has been reduced byconcentrating on the most informative feature elements.

15. Starting with random cluster assignments, perform K-means Euclideanclustering of the projected vectors r_(i) obtained in Step 14 to obtainpreliminary prototype distributions in the R-dimensional space, referredto as the chirographic space.

16. Starting with the preliminary prototype distributions of Step 15,perform K-means Gaussian clustering of the projected vectors obtained inStep 14, so as to obtain final Gaussian prototype distributions in thechirographic space. Denote these prototype distributions as g_(k), anduse cluster sizes to estimate the prior probability Pr(g_(k)) of eachprototype distribution.

17. Using the Gaussian distributions from Step 16, determine for allvectors r_(i) obtained in Step 14 the quantity Pr(r_(i) |g_(k)). Alsoestimate the probability of each feature vector as: ##EQU6## assumingthe total number of clusters is K. 18. Using the results of Steps 16 and17, compute the quantity: ##EQU7## and note against which charactera_(j) each frame r_(i) is aligned in the training data.

19. For each character a_(j) in the vocabulary considered, pool togetherall the r_(i) which have been aligned against it and accumulate thecorresponding Pr(g_(k) | r_(i)). After normalization, this provides anestimate of Pr(g_(k) |a_(j)), the prior probability of each prototypedistribution given each character a_(j).

The execution of Step 19 indicates the end of the training phase.

Decoding Phase

1. Splice the incoming data for a given writer to generate each class ofthe feature vectors, F_(x), F_(y) and F_(cg) in the same fashion asdescribed above. These classes are analogous to the codebooks describedabove with respect to the dynamic feature vector extraction method. Thefollowing Steps 2 through 4 are performed for each codebook.

2. Project onto a lower dimensional space as in Step 14 using theeigenvectors calculated in Step 13 of the training phase. This producestest feature vectors in the same chirographic space as the trainingdata.

3. Using the Gaussian distributions from Step 16, as well as the priorprobabilities from Step 19, determine, for all vectors obtained in theprevious step, a single Gaussian mixture distribution covering theentire chirographic label alphabet. This is illustrated below for thecodebook associated with the x slices i.e. F_(x) : ##EQU8## 4. Bymultiplying the scores of successive frames within the block of imagedata under analysis there is obtained the overall likelihood score forthat block, thus completing the decoding process for a given codebook;i.e. ##EQU9## where s_(d) represents a block of image data. 5. The finala posteriori probability for a block s_(d) given a character a_(j), andconsidering the contribution of all three codebooks, is given by:##EQU10##

Combination of Static and Dynamic Scores (Overall Likelihood Estimator28c)

Discrete character case (W1 and W2 of FIG. 1)

In that segmentation is implicit in this method, the output of thestatic recognizer, at the character level, can be employed to estimatethe a posteriori probability of the entire unknown character U. Thens_(d), as described above, encompasses the entire character. This can becombined with the a posteriori probability of the unknown characterusing the dynamic features by assuming that the two sources ofinformation are independent. The additional information is treated asarising from an independent codebook. Thus,

    Pr(U|a.sub.j)=Pr(U.sub.t |a.sub.j).sup.1/2 Pr(U.sub.d |a.sub.j).sup.1/2,

where Pr(U_(d) |a_(j)) is determined as in Step 5 of the Decoding Phaseset forth above, and where Pr(U_(t) |a_(j)) is determined as describedin Step 16 of the dynamic method. Note that it is not necessary toweight the static and dynamic contribution equally.

Unconstrained character case.

In the more general case, it is not generally possible to obtain asegmentation of the input stream that is natural for both the static andthe dynamic portions of the front-end parameter extraction block 22. Assuch, the following technique may be used.

1. Perform the dynamic decoding as set forth above for the dynamicfeature vector extraction case on all available input frames w_(t), andobtain Pr(w_(t) |a_(j)) ∀j, ∀t.

2. Process the image data by blocks generating Pr(s_(d) |a_(j)) ∀j foreach block using the static character model.

3. For each block s identify all of the frames w_(t) that lie withinthat image block.

4. Define ##EQU11## where T is the number of frames of w_(t) within s.5. The a posteriori probability of an image block s given a_(j) can thenbe written as:

    Pr(s|a.sub.j)=Pr(s.sub.t |a.sub.j).sup.α Pr(s.sub.d |a.sub.j).sup.1-60.

Reference is now made to FIG. 4 which is a detailed block diagram of thefront-end parameter extraction block 22 that is shown generally in FIG.3. The parameter extraction block 22 includes two processors 22a and 22bthat operate in parallel with one another, with processor 22a performingdynamic parameter extraction and processor 22b performing staticparameter extraction. The operation of the dynamic processor 22a isdescribed first.

Each sampled point of handwriting is represented by a point which isdefined by coordinates x_(n) and y_(n). This coordinate pair is providedto a pre-filtering block 34, which performs step 1 of both the dynamicand the static handwriting recognition methods set forth above. Thepoints are ballistically spaced as shown in FIG. 5. That is, the spacingof the points is a function of the velocity or speed of writing whichthe writer used to form the current character. For a variety of reasons,writers are seldom consistent in their velocity or writing speed, whichmay introduce high error rates in handwriting recognition. Thepre-filtering block 34 normalizes the points of FIG. 5 to provideequally spaced points x_(m) and y_(m) comprising a character, as shownin FIG. 6. Points x_(m) and y_(m) are provided to a dynamic parameterextraction block 36a, which performs Steps 2 and 3 of the dynamichandwriting recognition method for providing the vector v_(m). Detailsof this parameter extraction are described below relative to FIGS. 11,12, 13 and 14. The vector v_(m) is provided to a windowing block 38a,which performs Steps 4 and 5 of the dynamic handwriting recognitionmethod, for providing a spliced vector S_(i). Details of how the splicedvector S_(i) is provided is described below relative to FIGS. 14, 15,and 16. The spliced vector S_(i) is provided to a projection block 40a,which performs Steps 6-9 of the dynamic handwriting recognition method,for producing a feature vector r_(i). This eliminates redundancy in thespliced parameter vectors. Details of the function of block 40a are setforth relative to FIG. 17. Projection block 40a responds to the splicedvector S_(i) to provide a feature vector r_(i) which is provided to thedynamic prototype construction block 24a and the dynamic likelihoodestimator 28a, as previously explained with respect to FIG. 3. Detailsof projection block 40a are set forth relative to the flow chart of FIG.17.

Details of how the ballistically spaced character of FIG. 5 isnormalized by pre-filtering block 34 (FIG. 4) to produce the equallyspaced character of FIG. 6 is now explained relative to FIGS. 7 and 8,which illustrate how Step 1 of the handwriting recognition method isperformed. FIG. 7 is representative of the upper 1/4 curved portion ofFIG. 5. First, the density of points is increased by performing someinterpolation between the original raw points (denoted by a dot). Thisresults in a sequence of points comprising the set of original rawpoints (•) and the interpolated points (|). Then, filtering isaccomplished by a priori determining that equal spacing between pointsis a distance r suitably related to the distance between two pels asmanifested on the electronic tablet 14 (FIG. 3). In FIG. 7, this resultsin a sequence of points, after filtering, denoted by an X (at 56). Rawand interpolated points are considered to be at equally-spaced integerpoints n, and filtered points are considered to be at equally-spacedinteger points m.

With respect to FIG. 8, at block 42 the position at n=1 at the first(raw) point 48 of the stroke is designated as m=1, considered also thefirst filtered point. The second point 50 of the stroke at n=2 is thefirst point to be tested for filtering. At block 44 the (Euclidean)distance between the points m and n is determined according to therelationship:

    distance=|x.sub.n -x.sub.m |.sup.2 +|y.sub.n -y.sub.m |.sup.2

At block 46 a determination is made as to whether the determineddistance is greater than R. With reference to FIG. 7, point m=1 is point48 and point n=2 is point 50. It can be seen that distance is less thanR in FIG. 7, therefore the point is rejected and the method proceeds toblock 52 where n is incremented to 3, point 54. Distance is againcomputed in block 44 and compared with R in block 46. Eventually thedistance becomes greater than R, so the point 56 is accepted (m is madeequal to n in block 58). At block 60 the point (x_(n),y_(n)) is storedas a filtered point (x_(m),y_(m)), point 56, which is the 12th point. Atblock 62 n is incremented by 1, and a return is made to block 44 whereraw and interpolated points are treated as explained above.

FIGS. 11, 12, 13 and 14 illustrate how parameter extraction, block 36aof FIG. 4, which performs Steps 2 and 3 of the dynamic handwritingrecognition algorithm, is derived for providing a parameter vectorv_(m). FIG. 11 shows the local parameter extraction, FIG. 12 the localparameter vector, FIG. 13 is the global parameter extraction, and FIG.14 the global parameter vector. There are 6 local coordinates in thelocal parameter vector and 3 global coordinated in the global parametervector, for a total of 9 coordinates. For the local parameter vector,calculations are made relative to a current point 64 relative toprevious points 66 and 67 and following points 68 and 69. The specificcalculation for local parameter vectors are shown in FIG. 12. For theglobal parameter vector, calculations are made relative to a currentpoint 64 relative to baseline 65, initial point of the character 66,last point of the first stroke 67, and the first point of the secondstroke 68. The specific calculation for global parameter vector areshown in FIG. 14. Without loss of generality, the ensuing descriptionillustrates the handwriting recognition method for one codebook only,i.e., either the local parameter vectors or the global parametervectors.

Details of the windowing block 38a of FIG. 4 are now set forth relativeto FIGS. 15 and 16 to show how feature events are extracted from thedata. A small number of approximately equidistant feature points aredetermined using the same algorithm as in FIG. 8, but with a differentvalue of R, and parameter vectors are spliced at those points. Thenumber (2H+1) of parameter vectors to be spliced at each point isdetermined a priori, which in turn specifies the splicing dimensionQ=(2H+1)P.

Referring to FIG. 15, feature points are shown by dots, and windowcenters are shown by an X. Dots are referenced as points k, and X's arereferenced by index i as points k_(i). With respect to FIG. 16, at block70 i and a counter j are each set equal to 1. At block 72, k is set tok_(i) -H and at block 74 the corresponding v_(k) (of dimension P) isobtained. A determination is then made at block 76 whether or not (2H+1)v_(k) have been seen. If so, j is reinitialized to 1 and i isincremented by 1 in block 78 and the procedure repeats as justexplained. If not, v_(k) is appended to V_(i) starting at position (j-1)P+1. k and j are both incremented by 1 in block 82 and a return is madeto block 74 to get the next v_(k), and the procedure repeats as justexplained.

Referring to FIG. 17 the function of the projection block 40a of FIG. 4,which performs steps 6-9 of the dynamic handwriting recognition method,is explained in detail. The projection block is utilized to eliminateredundancy in the splice parameter vectors from the windowing block 38.A covariance matrix is computed for all spliced vectors in block 71, andthe associated eigenvalue and eigenvectors are found through principalcomponent analysis, in block 75. Using the R leading eigenvalues andeigenvectors of block 75, the spliced vectors are projected in block 77onto a subspace of smaller dimension called chirographic space,resulting in the projected vectors r_(i). How a covariance matrix iscomputed is described in "Matrix Computations" by J. H. Golub and C. F.Van Loan, John Hopkins, University Press, Baltimore, 1989. Thisreference also teaches how to perform a principal component analysis atblock 73, and how to project all S_(i) at block 77.

The chirographic space is then partitioned as shown in FIGS. 18 and 19,which details the prototype construction block 24a of FIG. 3, to producechirographic prototypes. The feature vectors are provided to block 79 toperform k-means Euclidean clustering. Details of block 79 are set forthrelative to FIGS. 19 and 20. The results of Euclidean clustering areprovided to block 81 to perform k-means Gaussian clustering to provideprototype distributions π_(k). Details of block 81 are set forthrelative to FIG. 21. FIGS. 18-21 detail how steps 10 and 11 of thedynamic handwriting recognition method are performed.

The prototype distributions or chirographic prototypes are provided tothe dynamic likelihood estimator 28a (FIG. 3) to produce candidatecharacters to decoder 30 (FIG. 3), if operating only with dynamicfeature vectors, or to provide input to the overall likelihood estimator28c if operating with joint static and dynamic feature vectors.

How to generally accomplish k-means clustering is described in"Clustering Algorithms" by J. A. Hartigan, J. Wiley, 1975.

FIG. 19 illustrates a space 83 which is divided into clusters 84, 86 and88. Each cluster includes a plurality of vectors indicated as points x,with a centroid being computed for each such cluster of vectors.

FIG. 20 details block 79 of FIG. 18. A number of random seeds, chosen tobe 250, is picked at block 90 from all points in the chirographic spaceobtained from block 22 in FIG. 3. The Euclidean distance between eachpoint and each seed is calculated at block 92. By assigning each pointto its closest seed, the space is partitioned into clusters at block 94.This corresponds to the clusters 84, 86 and 88 of FIG. 19. The centroidof each cluster is computed at block 96. This corresponds to the in FIG.19. These centroids are set to replace the original seeds at block 98.At decision block 100 a determination is made if the maximum number ofiterations is reached. If not, a return is made to block 92 and thesteps are repeated as just described. If so, the calculation of theEuclidean clustering is complete.

Reference is now made to FIG. 21 which details the Gaussian clusteringblock 81 of FIG. 18. The Euclidean clusters obtained in block 79 (FIG.18) are provided at block 102. The Gaussian distance between each pointand each centroid is calculated at block 104. By assigning each point toits closest centroid, the space is partitioned into clusters at block106. The new centroid of each cluster is computed at block 108. Atdecision block 110 a determination is made if the maximum number ofiterations is complete. If not, a return is made set to replace theoriginal seeds at block 98 (FIG. 20). At decision block 100 adetermination is made if the maximum number of iterations is reached. Ifnot, a return is made to block 92 and the steps are repeated as justdescribed. If so, the calculation of the Euclidean clustering iscomplete.

Reference is made to FIG. 21 which details the Gaussian clustering block81 of FIG. 18. The Euclidean clusters obtained in block 79 (FIG. 18) areprovided at block 102. The Gaussian distance between each point and eachcentroid is calculated at block 104. By assigning each point to itsclosest centroid, the space is partitioned into clusters at block 106.The new centroid of each cluster is computed at block 108. At decisionblock 110 a determination is made if the maximum number of iterations iscomplete. If not, a return is made to block 104 and the steps arerepeated as just described. If so, the calculations of the Gaussianclustering is complete. This results in final prototype distributions inchirographic space.

Refer to FIG. 22, which performs step 16 of the handwriting recognitiontechnique for one codebook only, and which illustrates how informationresulting from steps 12 and 13 of the dynamic handwriting recognitionmethod is operated on by the dynamic likelihood estimator 28a of FIG. 3to produce candidate characters for the decoder 30. At block 114 avariable i, which is indicative of the current frame (or window center),is initialized to 1, and the dynamic test feature vector is providedfrom the front end parameter extraction 22 (FIG. 4) as indicated atblock 116. At block 118 a variable k representative of the currentprototype distribution is initialized to k=1. The conditionalprobability of this feature vector given this prototype distribution iscomputed at block 120 and is provided to block 122.

The prototype construction block 24a (FIG. 3) of the training phase asrepresented by the chirographic prototype distributions II_(k) in block124 and mixture coefficients Pr(II_(k) |a_(j)) in block 126 are alsoprovided to block 122 where the combined probability is computed andstored. At decision block 128 a determination is made if k has reachedthe maximum number of clusters. If not, k is incremented by 1 asindicated at block 130, and a return is made to block 120 and the justrecited process is repeated. If so, the scores just stored areaccumulated at block 132 for all characters a_(j) in the underlyingalphabet. At decision block 134 a determination is made if all frames ihave been seen for the current character under consideration. If not, iis incremented by 1 at block 136 and a return is made to block 116 andthe just recited process is repeated. If so, the accumulated scores areordered in block 138 and a candidate list of characters a_(j) is formedfrom the top J scores for provision to the decoder 30 (FIG. 3).

Refer now to FIG. 23 which is a flow chart representation indicative ofthe operation of the decoder 30 (FIG. 3) for the case of decoding onlythe output of the dynamic likelihood estimator 28a of FIG. 3. A variablet, which is indicative of the current character under consideration, isinitialized to 1 at block 142. The candidate list of characters from thelikelihood estimator 28a (FIG. 3) for character C_(t) is provided atblock 144. A variable j indicative of the current candidate character isinitialized to 1 at block 146, and C_(t) is tentatively set equal toa_(j) at block 148. From the training block, Language Modelprobabilities 26 (FIG. 3) are provided at block 150. Based on theseprobabilities and previously recognized characters at block 154, thefinal score of the character a_(j) is computed at block 152. This scorerepresents the likelihood that C_(t) is recognized as a_(j) taking intoaccount the contextual information through the language model. Atdecision block 156 a determination is made if j=J, the index of the lastcandidate character in the candidate list provided by the likelihoodestimator 28. If not, a return is made to block 148 and the just recitedprocess is repeated. If so, final scores incorporating language modelprobabilities are ordered in block 158. The top candidate is selected asthe recognized answer for character C₁ in block 160. At decision block162 a determination is made if t=Tmax, the index of the last characterin the string to be recognized. If not, t is incremented by 1 in block164, to get the next character to be recognized. An update is made atblock 166, to insert the recognized C₁ in block 154, and a return ismade to block 144, with the just recited process being repeated. If so,the process is complete as indicated at block 168 and the whole stringof characters has been recognized.

Having described in detail the operation of the dynamic parameterextraction and evaluation functions of the handwriting recognizer ofFIG. 3, it is noted that Steps 1 and 12-19 of the static determinationoperate in the same manner, as do the corresponding blocks of the staticprocessor 22b of FIG. 4.

It is further noted that the Steps 2-11 of the static determinationmethod are not limited for use only with on-line handwriting systems,but may be employed to advantage in off-line systems wherein the inputsignals are not generated in real time. As an example, thespatially-based feature vector determination can be used in OpticalCharacter Recognition systems wherein a printed text is scanned andconverted to a digital format. Individual characters of the input may beprocessed to derive feature vectors, based on the shape of thecharacters, for subsequent recognition.

Two separate tasks were selected to evaluate the handwriting recognitionmethod that employs both static and dynamic processes. In the firsttask, eight writers were considered as part of a writer dependentexperiment. The recognizer was trained on data from a particular writerand then tested on an independent data set derived from the same writer.The second experiment was designed to ascertain the performance of thesystem in a writer independent mode. Data from all eight writers werepooled together and used to train the recognizer. The system was thentested on a set of four new writers that the recognizer had not beenexposed to. The test characters are drawn from the full 81 character(letter/digit/special symbols) set. Each test set consists ofapproximately 800 discrete characters. Recognition accuracy was measuredfor three different recognition techniques: the dynamic parameterizationtechnique described above, the static parameterization described above,and a combination of these two methods. These results are summarizedbelow, wherein Table 1 is for the writer dependent the case and Table 2for the writer independent case.

                  TABLE 1                                                         ______________________________________                                        Recognition results for the writer-dependent case.                            Dynamic        Static       Both                                              writer % err.  # err.  % err.                                                                              # err. % err.                                                                              # err.                              ______________________________________                                        MAR    5.6%    45      7.0%  56     4.4%  35                                  HIL    12.8%   103     12.1% 97     7.6%  61                                  VIV    11.1%   89      11.0% 88     3.7%  30                                  JOA    8.7%    70      9.2%  74     5.9%  47                                  ACY    15.1%   121     18.0% 145    10.6% 85                                  NAN    8.8%    71      12.2% 98     7.2%  58                                  LOY    5.4%    43      7.2%  58     3.6%  29                                  SAB    6.0%    48      5.7%  46     3.2%  26                                  TOTAL  9.2%    590     10.3% 662    5.8%  371                                 ______________________________________                                    

                  TABLE 2                                                         ______________________________________                                        Recognition results for the writer-independent case.                          Dynamic        Static       Both                                              writer % err.  # err.  % err.                                                                              # err. % err.                                                                              # err.                              ______________________________________                                        MAL    23%     184     24%   196    15%   122                                 BLA    19%     153     19%   154    11%    92                                 SAM    26%     207     24%   192    15%   123                                 WAR    10%      77     10%    80     4%    31                                 TOTAL  19%     621     19%   622    11%   368                                 ______________________________________                                    

The Tables show that although individually the dynamic and staticfront-end parameter extraction block 22 results in recognition rates,the joint use of static and dynamic information results in a significantreduction in the error rate. There is also observed a consistent drop inerror rate across all writers. Clearly, the static and dynamicinformation complement one another. This is borne out by analysis of theconfusion matrices. The static system was found to outperform thedynamic system for upper case characters, while the dynamic system tendsto make fewer errors for lower case characters. In both instances,nevertheless, fewer errors result when both systems are incorporatedinto the recognizer, than with either the static or dynamic front endalone.

Thus, while the invention has been particularly shown and described withrespect to presently preferred embodiments thereof, it will beunderstood by those skilled in the art that changes in form and detailsmay be made therein without departing from the scope and spirit of theinvention.

Having thus described our invention, what we claim as new, and desire tosecure by Letters Patent is:
 1. Handwriting recognition apparatus,comprising:handwriting transducer means having an output providing x-ycoordinate information generated by a writer while writing characters;first extracting means, having an input coupled to said output of saidhandwriting transducer means, for extracting and outputtingtemporally-based feature vectors from the x-y coordinate information;first training means, responsive to the temporally-based featurevectors, for providing and storing first corresponding characterprototypes based on K-means Euclidean clustering and K-means Gaussianclustering of the temporally-based feature vectors; second extractingmeans, having an input coupled to said output of said handwritingtransducer means, for extracting and outputting shape-based featurevectors from the x-y coordinate information; and second training means,responsive to the shape-based feature vectors, for providing and storingsecond corresponding character prototypes based on K-means Euclideanclustering and K-means Gaussian clustering of the shape-based featurevectors.
 2. Handwriting recognition apparatus, comprising:handwritingtransducer means having an output providing x-y coordinate informationgenerated by a writer while writing characters; first extracting means,having an input coupled to said output of said handwriting transducermeans, for extracting and outputting temporally-based feature vectorsfrom the x-y-coordinate information; first training means, responsive tothe temporally-based feature vectors, for providing first correspondingcharacter prototypes comprised of chirographic prototypes representingportions of characters and mixture coefficients indicating how tocombine the chirographic prototypes; second extracting means, having aninput coupled to said output of said handwriting transducer means, forextracting and outputting shape-based feature vectors from the x-ycoordinate information; and second training means, responsive to theshape-based feature vectors, for providing and storing secondcorresponding character prototypes based on K-means Euclidean clusteringand K-means Gaussian clustering of the shape-based feature vectors.